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It is possible to develop statistically signi cant relationships among variables that are completely unrelated in a causal sense For example, we might attempt to relate the shear strength of spot welds with the number of empty parking spaces in the visitor parking lot A straight line may even appear to provide a good t to the data, but the relationship is an unreasonable one on which to rely You can t increase the weld strength by blocking off parking spaces A strong observed association between variables does not necessarily imply that a causal relationship exists between those variables This type of effect is encountered fairly often in retrospective data analysis, and even in observational studies Designed experiments are the only way to determine causeand-effect relationships Regression relationships are valid only for values of the regressor variable within the range of the original data.

of factor indexes necessary for statistical significance Size of Discrepancy Necessary for Significance Factor Index Comparisons VCI vs. POI VCI vs. WMI POI vs. PSI p < .01 13 or more 13 or more 17 or more p < .05 10 12 10 12 13 16 Not Significant 0 90 0 90 0 12

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The linear relationship that we have tentatively assumed may be valid over the original range of x, but it may be unlikely to remain so as we extrapolate that is, if we use values of x beyond that range In other words, as we move beyond the range of values of x for which data were collected, we become less certain about the validity of the assumed model Regression models are not necessarily valid for extrapolation purposes Now this does not mean don t ever extrapolate There are many problem situations in science and engineering where extrapolation of a regression model is the only way to even approach the problem However, there is a strong warning to be careful A modest extrapolation may be perfectly all right in many cases, but a large extrapolation will almost never produce acceptable results..

[FH97]

score (to obtain Verbal scale range). Similarly, subtract the person s lowest Performance subtest scaled score from his or her highest Performance subtest scaled score (to obtain Performance scale range). The range of subtest scaled score of the Verbal and Performance scales must each be 8 or more points to be considered abnormal (see Table 11.6). When computing these scaled-score ranges, include only the scaled scores of the six subtests that comprise the V-IQ and the scaled scores of the five subtests that comprise the P-IQ. If you have substituted a supplemental Verbal or Performance subtest in the calculation of one of the IQs, then that substituted subtest should be used in the calculation of the range of subtest scaled scores. Scatter (i.e., abnormal variability) among Verbal subtests indicates that the client s Verbal IQ represents a summary of diverse abilities and does not represent a unitary entity. If an abnormal amount of scatter is present across subtest scores, a global verbal ability is not likely responsible for the individual s scaled scores. Similar logic applies to the Performance IQ. Thus, if unusually large scatter is present in either IQ scale, making at least one of the IQs uninterpretable, then the discrepancy between the V-IQ and P-IQ is not very meaningful or interpretable. To determine when the V-IQ versus P-IQ discrepancy can be interpreted, four questions must be answered: two about the Verbal scale and two about the Performance scale. Table 11.7 outlines the questions to ask about each IQ scale. First, examine the difference between the VCI and WMI to determine whether the discrepancy is signifi-

11-8.3

Lack-of-Fit Test (CD Only)

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